{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.dates as mdates\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from sympy import Symbol, symbols, Matrix, sin, cos\n",
    "from sympy import init_printing\n",
    "init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter Implementation for Constant Turn Rate and Velocity (CTRV) Vehicle Model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Wikipedia](http://en.wikipedia.org/wiki/Extended_Kalman_filter) writes: In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.\n",
    "\n",
    "$\\boldsymbol{x}_{k} = g(\\boldsymbol{x}_{k-1}, \\boldsymbol{u}_{k-1}) + \\boldsymbol{w}_{k-1}$\n",
    "\n",
    "$\\boldsymbol{z}_{k} = h(\\boldsymbol{x}_{k}) + \\boldsymbol{v}_{k}$\n",
    "\n",
    "Where $w_k$ and $v_k$ are the process and observation noises which are both assumed to be zero mean Multivariate Gaussian noises with covariance matrix $Q$ and $R$ respectively.\n",
    "\n",
    "The function $g$ can be used to compute the predicted state from the previous estimate and similarly the function $h$ can be used to compute the predicted measurement from the predicted state. However, $g$ and $h$ cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian matrix) is computed.\n",
    "\n",
    "At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Situation covered: You have a velocity sensor, which measures the vehicle speed ($v$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector - Constant Turn Rate and Velocity Vehicle Model (CTRV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constant Turn Rate, Constant Velocity Model for a vehicle ![CTRV Model](CTRV-Model.png)\n",
    "\n",
    "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate}} \\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "numstates=5 # States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n",
    "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "vs, psis, dpsis, dts, xs, ys, lats, lons = symbols('v \\psi \\dot\\psi T x y lat lon')\n",
    "\n",
    "gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))],\n",
    "             [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))],\n",
    "             [psis+dpsis*dts],\n",
    "             [vs],\n",
    "             [dpsis]])\n",
    "state = Matrix([xs,ys,psis,vs,dpsis])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This formulas calculate how the state is evolving from one to the next time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x + \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y + \\frac{v}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡    v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "⎢x + ───────────────────────────────────────⎥\n",
       "⎢                    \\dot\\psi               ⎥\n",
       "⎢                                           ⎥\n",
       "⎢    v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "⎢y + ────────────────────────────────────── ⎥\n",
       "⎢                   \\dot\\psi                ⎥\n",
       "⎢                                           ⎥\n",
       "⎢             T⋅\\dot\\psi + \\psi             ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                     v                     ⎥\n",
       "⎢                                           ⎥\n",
       "⎣                 \\dot\\psi                  ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the Jacobian of the Dynamic Matrix with respect to the state vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢  \\psi  ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎣\\dot\\psi⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & \\frac{v}{\\dot\\psi} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 1 & \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 0 & 1 & 0 & T\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      v⋅(-cos(\\psi) + cos(T⋅\\dot\\psi + \\psi))  -sin(\\psi) + sin(T⋅\\dot\\psi + \n",
       "⎢1  0  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                               \\dot\\psi        \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢      v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))  cos(\\psi) - cos(T⋅\\dot\\psi + \\\n",
       "⎢0  1  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                              \\dot\\psi         \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0  0                     1                                      0            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      1            \n",
       "⎢                                                                             \n",
       "⎣0  0                     0                                      0            \n",
       "\n",
       "\\psi)  T⋅v⋅cos(T⋅\\dot\\psi + \\psi)   v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "─────  ────────────────────────── - ───────────────────────────────────────⎥\n",
       "                \\dot\\psi                                   2               ⎥\n",
       "                                                   \\dot\\psi                ⎥\n",
       "                                                                           ⎥\n",
       "psi)   T⋅v⋅sin(T⋅\\dot\\psi + \\psi)   v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "────   ────────────────────────── - ────────────────────────────────────── ⎥\n",
       "                \\dot\\psi                                  2                ⎥\n",
       "                                                  \\dot\\psi                 ⎥\n",
       "                                                                           ⎥\n",
       "                                        T                                  ⎥\n",
       "                                                                           ⎥\n",
       "                                        0                                  ⎥\n",
       "                                                                           ⎥\n",
       "                                        1                                  ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has to be computed on every filter step because it consists of state variables!\n",
    "\n",
    "To Sympy Team: A `.to_python` and `.to_c` and `.to_matlab` whould be nice to generate code, like it already works with `print latex()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial Uncertainty $P_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialized with $0$ means you are pretty sure where the vehicle starts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1000.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,  1000.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,  1000.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,  1000.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,  1000.]]), (5, 5))\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAFMCAYAAAD1D2YBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107e65650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\n",
    "print(P, P.shape)\n",
    "\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Noise Covariance Matrix Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"*The state uncertainty model models the disturbances which excite the linear system. Conceptually, it estimates how bad things can get when the system is run open loop for a given period of time.*\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  3.09760000e-06,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   3.09760000e-06,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   4.00000000e-06,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          3.09760000e-02,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   4.00000000e-04]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "sGPS     = 0.5*8.8*dt**2  # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sCourse  = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle\n",
    "sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sYaw     = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle\n",
    "\n",
    "Q = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2])\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVgAAAFCCAYAAAC0IcW9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAQ2n/hcVhBWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10808c190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(8))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(8))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read '2014-03-26-000-Data.csv' successfully.\n"
     ]
    }
   ],
   "source": [
    "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n",
    "datafile = '2014-03-26-000-Data.csv'\n",
    "\n",
    "date, \\\n",
    "time, \\\n",
    "millis, \\\n",
    "ax, \\\n",
    "ay, \\\n",
    "az, \\\n",
    "rollrate, \\\n",
    "pitchrate, \\\n",
    "yawrate, \\\n",
    "roll, \\\n",
    "pitch, \\\n",
    "yaw, \\\n",
    "speed, \\\n",
    "course, \\\n",
    "latitude, \\\n",
    "longitude, \\\n",
    "altitude, \\\n",
    "pdop, \\\n",
    "hdop, \\\n",
    "vdop, \\\n",
    "epe, \\\n",
    "fix, \\\n",
    "satellites_view, \\\n",
    "satellites_used, \\\n",
    "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n",
    "                  converters={1: mdates.strpdate2num('%H%M%S%f'),\n",
    "                              0: mdates.strpdate2num('%y%m%d')},\n",
    "                  skiprows=1)\n",
    "\n",
    "print('Read \\'%s\\' successfully.' % datafile)\n",
    "\n",
    "# A course of 0° means the Car is traveling north bound\n",
    "# and 90° means it is traveling east bound.\n",
    "# In the Calculation following, East is Zero and North is 90°\n",
    "# We need an offset.\n",
    "course =(-course+90.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Function H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix $J_H$ is the Jacobian of the Measurement function $h$ with respect to the state. Function $h$ can be used to compute the predicted measurement from the predicted state.\n",
    "\n",
    "If a GPS measurement is available, the following function maps the state to the measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎣\\dot\\psi⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hs = Matrix([[xs],\n",
    "             [ys],\n",
    "             [vs],\n",
    "             [dpsis]])\n",
    "hs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0  0  0  0⎤\n",
       "⎢             ⎥\n",
       "⎢0  1  0  0  0⎥\n",
       "⎢             ⎥\n",
       "⎢0  0  0  1  0⎥\n",
       "⎢             ⎥\n",
       "⎣0  0  0  0  1⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JHs=hs.jacobian(state)\n",
    "JHs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If no GPS measurement is available, simply set the corresponding values in $J_h$ to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Noise Covariance $R$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[  3.60000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   3.60000000e+01,   0.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "           1.00000000e-02]]), (4, 4))\n"
     ]
    }
   ],
   "source": [
    "varGPS = 6.0 # Standard Deviation of GPS Measurement\n",
    "varspeed = 1.0 # Variance of the speed measurement\n",
    "varyaw = 0.1 # Variance of the yawrate measurement\n",
    "R = np.matrix([[varGPS**2, 0.0, 0.0, 0.0],\n",
    "               [0.0, varGPS**2, 0.0, 0.0],\n",
    "               [0.0, 0.0, varspeed**2, 0.0],\n",
    "               [0.0, 0.0, 0.0, varyaw**2]])\n",
    "\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAAEnCAYAAAATun62AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10841d890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4.5, 4.5))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(numstates)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approx. Lat/Lon to Meters to check Location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RadiusEarth = 6378388.0 # m\n",
    "arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/°\n",
    "\n",
    "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n",
    "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n",
    "\n",
    "mx = np.cumsum(dx)\n",
    "my = np.cumsum(dy)\n",
    "\n",
    "ds = np.sqrt(dx**2+dy**2)\n",
    "\n",
    "GPS=np.hstack((True, (np.diff(ds)>0.0).astype('bool'))) # GPS Trigger for Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.        ],\n",
      "        [ 0.        ],\n",
      "        [-4.08756111],\n",
      "        [ 0.67322222],\n",
      "        [-0.32660346]]), (5, 1))\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUoAAAAWCAYAAACmEtU9AAAABHNCSVQICAgIfAhkiAAABThJREFU\neJztnF2IFlUYx3+2WybWpmZJ3+L6URCUW5TEtrQ3ERERhBehSV1VVBBRFFvIG2V20wcFEdRFaKRR\nURQSSRSEeSFmqXUjyFJptu1mZW6RpdvFMyNnTjPvnDNn9j3H2fMDmX3PeZ73POfPM/POOfOMEIlE\nIpG2TCtovxAYAN6oaZwlwFrgO2ACmAs8DIzU6GtqdxXwKDADOB/YBqwG9lvOqVO4aGfj31T9XAkp\nd5cBdwF/IfrPANYAuy3n1ClCy90y/bqAZ4Eh4M+y4M4A1gMnG07G5Pv2ASuVtiHgG+CUmnxN7fqA\nzcCs5PNpwOfAz8D80pl0HhftbPybqp8rIeXuUuAD4FSl7WXgEHB5SSw+CC13TfVbDKwziI+XkBOi\nLtYgJ1K30jYH+Ae4pyZfU7tNwEJtjKXIr9DGklh84KKdjX9T9XMlpNx9HtF5udJ2U9L2YkksPggt\nd230awG3twtuAfBJyQRs2QN8mNO+G/i0Jl9Tu8PA98DZmt2vwFhJLD5w0c7Gv6n6uRJS7q4Cfgeu\nV9puQ070Z0pi8UFouWuj31xgF7IUB+AkzeBeZNldF6cDi5CTS+dH4IoafG3GGAbmATM1u7+R/YqQ\ncNHOxr+p+rkSWu6uQ5aZm5W2PuAosKFNLD4IMXdt9BtD9twH0wb9QnkjsKXdDCy5KDkeyukbB3qA\n6Y6+NmMsS+yHFZtzkZN/W0EcvnDRzsa/qfq5Elru6vQCdwD3AzsLbHwRYu7qlOn3BXBz+kG9UJ6H\nLKn2FnxxFXqS45GcvvHkOCunz8bXZoxx4CfN5j7gGPBYQRy+cNHOxr+p+rkSWu6m3II8R/gIeA54\npSAGn4SYuymm+n2NckeqXijnI5uidXI0OU7k9KVP1bty+mx8XcZYgPyirAW2Ftj4wmVeNv5N1c+V\nUHP3fUTzS5H9ti3AmQVx+CLk3DXV7xdkWQ9knxTNQzY7dS4DXqe45lLnK+DO5O/RNnbpPtcfBf2m\nvlXHmA68CbwKPN7mO3zhop2Nf1P1g+bmLshd1BPAZ8hd0fICOx+EnrtQrt9BZE8TyF4ou5EllM5O\npASkCiPI1X52Tt9M4DeKJ2Lqe6ziGK8hG7uri8P3iot2Nv5N1Q+albsXI3WBuxSbHcnxVqSm9XBB\nPJ0mxNy11a8beUgJZJfeowUDujCO/EpfkNO3ENkHcPWtMkYLKStQT/JVbWLxgYt2Nv5N1c+VkHK3\nJ7HbgTyESEmXntNov5TtNKHlbhX9ZqNsRaoXyv1Mzl7HJuBqssufXmRy72i2i8iWmZj62oyxEpn3\nk1p7v/Z5Cdkqfh+4aGfj31T9XAkld48gdzjDSM1qyiXJcTvZbbMQtA8pd231AzgL+OH/05KBDiDl\nHnVyDnILrFa6vwB8S/YVowHkVvrjCr42Y4wi77Cr/zaSraUaRG7p3zWY32Tiop2Nf1P1cyWk3H0a\neIDsBWE9sly8UmkLRfvQctdUP9X+eCG6ukc5gew5XQu8leNYlQPAdcirRn1Ikegc4Aayj/VHkJNw\nbwVfU7v3kvYVOXE+pcUyRnlh7GTjop2Nf1P1cyWk3B1C6v42AP8iD18PJj57tFhC0D603DXVL6Uf\neKRoctcAbxd1TkFavgM4wWn5DmAK0/IdwAlML/Cl2qC/mbMVqT/qJQLt3x6IlBP180fUvjoPIneg\nx9EvlAAPIRv1prVnTWUQ7VclYkXUzx9R++oMIP/zkL5nmks/cPekhhM23cjbJpFqRP38EbWvThfy\n8kRIpVaRSCQSiUQikUgkEolMBf4DWgW1csY3di4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( -0.002, \\quad 0.002, \\quad -0.003, \\quad 0.003\\right )$$"
      ],
      "text/plain": [
       "(-0.002, 0.002, -0.003, 0.003)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102203150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi]]).T\n",
    "print(x, x.shape)\n",
    "\n",
    "U=float(np.cos(x[2])*x[3])\n",
    "V=float(np.sin(x[2])*x[3])\n",
    "\n",
    "plt.quiver(x[0], x[1], U, V)\n",
    "plt.scatter(float(x[0]), float(x[1]), s=100)\n",
    "plt.title('Initial Location')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put everything together as a measurement vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 10800)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi))\n",
    "# Lenth of the measurement\n",
    "m = measurements.shape[1]\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "x0 = []\n",
    "x1 = []\n",
    "x2 = []\n",
    "x3 = []\n",
    "x4 = []\n",
    "x5 = []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "dstate=[]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\end{bmatrix} =  \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4]  \\end{matrix}}_{\\textrm{Python Nomenclature}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "\n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    # see \"Dynamic Matrix\"\n",
    "    if np.abs(yawrate[filterstep])<0.0001: # Driving straight\n",
    "        x[0] = x[0] + x[3]*dt * np.cos(x[2])\n",
    "        x[1] = x[1] + x[3]*dt * np.sin(x[2])\n",
    "        x[2] = x[2]\n",
    "        x[3] = x[3]\n",
    "        x[4] = 0.0000001 # avoid numerical issues in Jacobians\n",
    "        dstate.append(0)\n",
    "    else: # otherwise\n",
    "        x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2]))\n",
    "        x[1] = x[1] + (x[3]/x[4]) * (-np.cos(x[4]*dt+x[2])+ np.cos(x[2]))\n",
    "        x[2] = (x[2] + x[4]*dt + np.pi) % (2.0*np.pi) - np.pi\n",
    "        x[3] = x[3]\n",
    "        x[4] = x[4]\n",
    "        dstate.append(1)\n",
    "    \n",
    "    # Calculate the Jacobian of the Dynamic Matrix A\n",
    "    # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n",
    "    a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n",
    "    a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    JA = np.matrix([[1.0, 0.0, a13, a14, a15],\n",
    "                    [0.0, 1.0, a23, a24, a25],\n",
    "                    [0.0, 0.0, 1.0, 0.0, dt],\n",
    "                    [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    \n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = JA*P*JA.T + Q\n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Measurement Function\n",
    "    hx = np.matrix([[float(x[0])],\n",
    "                    [float(x[1])],\n",
    "                    [float(x[3])],\n",
    "                    [float(x[4])]])\n",
    "\n",
    "    if GPS[filterstep]: # with 10Hz, every 5th step\n",
    "        JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 1.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    else: # every other step\n",
    "        JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0]])        \n",
    "    \n",
    "    S = JH*P*JH.T + R\n",
    "    K = (P*JH.T) * np.linalg.inv(S)\n",
    "\n",
    "    # Update the estimate via\n",
    "    Z = measurements[:,filterstep].reshape(JH.shape[0],1)\n",
    "    y = Z - (hx)                         # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "\n",
    "    # Update the error covariance\n",
    "    P = (I - (K*JH))*P\n",
    "\n",
    "\n",
    "    # Save states for Plotting\n",
    "    x0.append(float(x[0]))\n",
    "    x1.append(float(x[1]))\n",
    "    x2.append(float(x[2]))\n",
    "    x3.append(float(x[3]))\n",
    "    x4.append(float(x[4]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))    \n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x108009dd0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7MAAAIyCAYAAAAZhZ2mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1080c3d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.semilogy(range(m),Px, label='$x$')\n",
    "plt.step(range(m),Py, label='$y$')\n",
    "plt.step(range(m),Pdx, label='$\\psi$')\n",
    "plt.step(range(m),Pdy, label='$v$')\n",
    "plt.step(range(m),Pddx, label='$\\dot \\psi$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAGRCAYAAAAwxyelAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10847c790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7sAAAIwCAYAAABHmnxZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFwAAAAAQnP8DGQIFKHoxVfoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ac5f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.step(range(len(measurements[0])),Kx, label='$x$')\n",
    "plt.step(range(len(measurements[0])),Ky, label='$y$')\n",
    "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n",
    "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n",
    "\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(prop={'size':18})\n",
    "plt.ylim([-0.1,0.1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8YAAAO5CAYAAADb5TzVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109700190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "plt.subplot(411)\n",
    "plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n",
    "plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n",
    "\n",
    "plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "plt.ylabel('Position (relative to start) [m]')\n",
    "\n",
    "plt.subplot(412)\n",
    "plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n",
    "plt.ylabel('Course')\n",
    "plt.legend(loc='best',prop={'size':16})\n",
    "           \n",
    "plt.subplot(413)\n",
    "plt.step(range(len(measurements[0])),x3, label='$v$')\n",
    "plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)')\n",
    "plt.ylabel('Velocity')\n",
    "plt.ylim([0, 30])\n",
    "plt.legend(loc='best',prop={'size':16})\n",
    "\n",
    "plt.subplot(414)\n",
    "plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n",
    "plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)')\n",
    "plt.ylabel('Yaw Rate')\n",
    "plt.ylim([-0.6, 0.6])\n",
    "plt.legend(loc='best',prop={'size':16})\n",
    "plt.xlabel('Filter Step')\n",
    "\n",
    "plt.savefig('Extended-Kalman-Filter-CTRV-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%pylab --no-import-all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAAAWCAYAAACxMEX0AAAABHNCSVQICAgIfAhkiAAABT5JREFU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\n",
      "text/latex": [
       "$$\\left ( -100.0, \\quad 700.0, \\quad -50.0, \\quad 400.0\\right )$$"
      ],
      "text/plain": [
       "(-100.0, 700.0, -50.0, 400.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7oAAAIwCAYAAACoWBdnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083af410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "# EKF State\n",
    "plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='k', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "# Start/Goal\n",
    "plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n",
    "plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.ylabel('Y [m]')\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "plt.axis('equal')\n",
    "#plt.tight_layout()\n",
    "\n",
    "#plt.savefig('Extended-Kalman-Filter-CTRV-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Detailed View"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10969b650>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtkAAAEeCAYAAABfSAkPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7P8BQ5E2l6/HawUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c431490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,9))\n",
    "\n",
    "plt.subplot(221)\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(70, 130)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(140, 200)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "\n",
    "\n",
    "plt.subplot(222)\n",
    "\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(160, 260)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(110, 160)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Write Google Earth KML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert back from Meters to Lat/Lon (WGS84)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "latekf = latitude[0] + np.divide(x1,arc)\n",
    "lonekf = longitude[0]+ np.divide(x0,np.multiply(arc,np.cos(latitude*np.pi/180.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data for KML Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coordinates and timestamps to be used to locate the car model in time and space\n",
    "The value can be expressed as yyyy-mm-ddThh:mm:sszzzzzz, where T is the separator between the date and the time, and the time zone is either Z (for UTC) or zzzzzz, which represents ±hh:mm in relation to UTC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "car={}\n",
    "car['when']=[]\n",
    "car['coord']=[]\n",
    "car['gps']=[]\n",
    "for i in range(len(millis)):\n",
    "    d=datetime.datetime.fromtimestamp(millis[i]/1000.0)\n",
    "    car[\"when\"].append(d.strftime(\"%Y-%m-%dT%H:%M:%SZ\"))\n",
    "    car[\"coord\"].append((lonekf[i], latekf[i], 0))\n",
    "    car[\"gps\"].append((longitude[i], latitude[i], 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from simplekml import Kml, Model, AltitudeMode, Orientation, Scale, Style, Color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The model path and scale variables\n",
    "car_dae = r'https://raw.githubusercontent.com/balzer82/Kalman/master/car-model.dae'\n",
    "car_scale = 1.0\n",
    "\n",
    "# Create the KML document\n",
    "kml = Kml(name=d.strftime(\"%Y-%m-%d %H:%M\"), open=1)\n",
    "\n",
    "# Create the model\n",
    "model_car = Model(altitudemode=AltitudeMode.clamptoground,\n",
    "                            orientation=Orientation(heading=75.0),\n",
    "                            scale=Scale(x=car_scale, y=car_scale, z=car_scale))\n",
    "\n",
    "# Create the track\n",
    "trk = kml.newgxtrack(name=\"EKF\", altitudemode=AltitudeMode.clamptoground,\n",
    "                     description=\"State Estimation from Extended Kalman Filter with CTRV Model\")\n",
    "\n",
    "# Attach the model to the track\n",
    "trk.model = model_car\n",
    "trk.model.link.href = car_dae\n",
    "\n",
    "# Add all the information to the track\n",
    "trk.newwhen(car[\"when\"])\n",
    "trk.newgxcoord(car[\"coord\"])\n",
    "\n",
    "# Style of the Track\n",
    "trk.iconstyle.icon.href = \"\"\n",
    "trk.labelstyle.scale = 1\n",
    "trk.linestyle.width = 4\n",
    "trk.linestyle.color = '7fff0000'\n",
    "\n",
    "# Add GPS measurement marker\n",
    "fol = kml.newfolder(name=\"GPS Measurements\")\n",
    "sharedstyle = Style()\n",
    "sharedstyle.iconstyle.icon.href = 'http://maps.google.com/mapfiles/kml/shapes/placemark_circle.png'\n",
    "\n",
    "for m in range(len(latitude)):\n",
    "    if GPS[m]:\n",
    "        pnt = fol.newpoint(coords = [(longitude[m],latitude[m])])\n",
    "        pnt.style = sharedstyle\n",
    "\n",
    "# Saving\n",
    "#kml.save(\"Extended-Kalman-Filter-CTRV.kml\")\n",
    "kml.savekmz(\"Extended-Kalman-Filter-CTRV.kmz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exported KMZ File for Google Earth\n"
     ]
    }
   ],
   "source": [
    "print('Exported KMZ File for Google Earth')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
